Varying-Coefficient Stochastic Differential Equations with Applications in Ecology

Stochastic Differential Equations with Applications

Estimation for stochastic differential equations with a small diffusion coefficient

We consider a multidimensional diffusion X with drift coefficient b(Xt, α) and diffusion coefficient εa(Xt, β) where α and β are two unknown parameters, while ε is known. For a high-frequency sample of observations of the diffusion at the time points k/n, k = 1, . . . , n, we propose a class of contrast functions and thus obtain estimators of (α, β). The estimators are shown to be consistent an...

Stochastic Differential Equations and Applications

The expressions of solutions for general n × m matrix-valued inhomogeneous linear stochastic differential equations are derived. This generalizes a result of Jaschke (2003) for scalar inhomogeneous linear stochastic differential equations. As an application, some IR vector-valued inhomogeneous nonlinear stochastic differential equations are reduced to random differential equations, facilitating...

Applications of Stochastic Partial Differential Equations

s of the talks Robert Adler, Technion-Israel Institute of Technology, Israel On quantifying shape, with two applications to stochastic processes I shall discuss some classical Integral and Differential Geometric ways to classify shape, and describe 1. A new class of results about the excursion sets of smooth random fields which uses them. 2. An application of these classifiers to the study of t...

Conditioned Stochastic Differential Equations: Theory and Applications

We generalize the notion of brownian bridge. More precisely, we study a standard brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations which we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general pre...