Recent Advances in Stochastic Analysis and Control

Overview

We are delighted to announce the upcoming workshop

Recent Advances in Stochastic Analysis and Control

to be held at the University of 糖心TV, supported by the Centre for Research in Statistical Methodology (CRiSM) and the Heilbronn Institute for Mathematical Research.

This one-day workshop will bring together leading researchers to discuss recent developments in stochastic analysis, stochastic control, and their applications in finance and applied probability.

The conference takes place from 1 May 2026 at the University of 糖心TV, in Coventry.

You can register for the conference at the registration page up to the 27 of April or until the event reaches capacity. Registration is free of charge.

Invited speakers

Prof. Zhen-Qing Chen, University of Washington

Prof. , LSE

Prof. , University of Oxford

Prof.

Durham University

Prof. , Durham University

Prof. , Imperial College London

Schedule

All events will take place in the Mathematical Science Building. Details of how to find this are included on the Practicalities page.

Friday 1 May	Location	Event
9:30-10:00	MSB Atrium	Arrival and coffee
10:00-11:00	MSB007	Zhen-Qing Chen Title: Coupled time-fractional parabolic equations and probabilistic representation Abstract: Anomalous diffusion is observed across diverse natural systems, ranging from cellular signaling and animal foraging to contaminant transport in groundwater, and is closely related to time-fractional equations. In the first part of this talk, I will discuss these connections, specifically how fractional models arise naturally as scaling limits of random walks. I will then present some recent results on time-dependent, time-fractional parabolic equations and their probabilistic representations.
11:00-12:00	MSB007	Umut Cetin Title: Recurrent transformations of Markov processes Abstract: Partly motivated by problems in Monte-Carlo simulation of killed diffusion processes, we develop a theory of Girsanov transformations for a general (standard) Markov process X that turns them into recurrent processes while keeping the Markovian structure. To this end we consider transformations via multiplicative functionals of the form h(X) exp(A), where h is the potential function of a positive continuous additive functional C (PCAF)and A is another PCAF. We show that after the measure change, X is a recurrent Markov process if the Revuz measure of C is finite with compact support under a mild duality assumption. When X is a symmetric Markov process, a weaker integrability condition on h turns X into a recurrent process after the measure change. Based on a joint work with Zhen-Qing Chen.
12:00-1:00	MSB Atrium	Lunch
1:00-2:00	MSB007	Ben Hambly Title: Stochastic Stefan problems and limit order books Abstract: In electronic financial markets buyers and sellers post orders indicating how many units of asset they are prepared to buy or sell and at what price. The collection of all these posted orders is called the limit order book. Those who need to trade then take the best available price for either buying or selling. This mechanism gives rise to the evolution of asset prices that we see. From a simple model for the arrival and cancellation of limit orders, and taking scaling limits, we will show how it may be natural to model the limit order book as a stochastic Stefan problem. The Stefan problem arises as a model for the evolution of the temperature in two phases of a material. It is a partial differential equation with a free boundary describing the interface between the phases. By regarding the sides of the order book as different phases and driving them with white noise we can model the whole system as a pair of coupled stochastic partial differential equations and the price of the asset is then the interface between the phases. We will discuss the existence, uniqueness and properties of the motion of the interface for this stochastic Stefan problem.
2:00-3:00	MSB007	Harry Zheng Title: Reinforcement Learning for Speculative Trading under Exploratory Framework Abstract: We study a speculative trading problem within the exploratory reinforcement learning (RL) framework of Wang et al. (2020). The problem is formulated as a sequential optimal stopping problem over entry and exit times under general utility function and price process. We first consider a relaxed version of the problem in which the stopping times are modelled by the jump times of Cox processes driven by bounded, non-randomized intensity controls. Under the exploratory formulation, the agent's randomized control is characterized via the probability measure over the jump intensities, and their objective function is regularized by Shannon's differential entropy. This yields a system of the exploratory HJB equations and Gibbs distributions in closed form as the optimal policy. Error estimates and convergence of the RL objective to the value function of the original problem are established. Finally, an RL algorithm is designed, its implementation is showcased in a pairs-trading application. (Joint work with Alex Tse and Yun Zhao)
3:00-3:30	MSB Atrium	Coffee
3:30-4:30	MSB007	Huaizhong Zhao Title: Ergodic theory under nonlinear expectations Abstract: In this talk, I will discuss the ideas of ergodic theory of a dynamical system under the nonlinear expectation space/nonadditive probabilities. Ergodicity is defined as that any invariant set or its complement has upper probability 0 (Feng-Zhao (SIMA 2021)). It was proved that the ergodicity is equivalent to irreducibility, the eigenvalue 1 of the Koopman operator being simple, and Birkhoff鈥檚 law of large numbers with a single value. For a stochastic system under a sublinear Markov setup, the theory was also developed via lifting to canonical dynamical systems. Following this initial work, many progresses have been made recently. They include Zhao-Zhao (Preprint 2025) on the existence of invariant expectations of G-SDEs; Ma-Zhao (Preprint 2025) on ergodic optimal controls; Feng-Huang-Liu-Zhao (AAP 2026 and Preprint 2026) on the equivalence of the ergodicity and mixing of upper probability with the ergodicity of the invariant skeleton measure. If time permits, I will also talk about a weaker regime that any invariant set has upper probability 0 or 1 of Cerreia-Vioglio, Maccheroni and Marinacci (2016). We prove that this case does not give the irreducibility but is equivalent to a decomposition of finite ergodic components. I will also discuss Hurewicz鈥檚 problem on Birkhoff鈥檚 ergodic theorem for noninvariant measures and its necessary and sufficient conditions in terms of sublinear probabilities.
4:30-5:30	MSB007	Chunrong Feng Title: Ergodicity of non-stationary stochastic processes Abstract: As we know, many important works in ergodic theory of stochastic dynamical systems have been obtained for invariant measures and aperiodic stationary processes. However, there exist non-stationary but ergodic processes. I will discuss the ergodic theory of three kind of non-stationary stochastic processes, which are random periodic processes, random quasi-periodic processes and stochastic processes under nonlinear expectation spaces. My talk will mainly concentrate on random periodic processes and periodic measures. This talk is based on some joint work with Y. Liu, Y. J. Liu, Baoyou Qu, Huaizhong Zhao and Johnny Zhong.
6:00-8:00	Scarman	Dinner by invitation
		Conference Booklet

Organisers

Andreas Kyprianou, Gechun Liang, Aleksandar Mijatovic, .