Related papers: Jump Processes with Deterministic and Stochastic C…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate,…
This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
A deterministic walk in a random environment can be understood as a general random process with finite-range dependence that starts repeating a loop once it reaches a site it has visited before. Such process lacks the Markov property. We…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…
We address the stabilization of both classical and quantum systems modeled by jump-diffusion stochastic differential equations using a novel hysteresis switching strategy. Unlike traditional methods that depend on global Lyapunov functions…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic…