Stochastic reaction networks in stochastic environment

Abstract: In the typical definition of stochastic reaction networks, the rate functions only depend on the current state and do not change over time. However this is not true in many biological systems, where the rate functions change over time. In this study we considered the more general case of the rates depending on both the current configuration and another stochastic process, which we call "environment" and is not directly affected by the system of interest. We study the positive recurrence of this more general model under the assumption of "monomolecularity", and under certain conditions characterize the stationary distribution (when it exists) as a mixture of Poisson distributions, which is uniquely identified as the law of a fixed point of a stochastic recurrence equation. This recursion can be utilized for numerical computation of moments and other distributional features.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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