Hitting probabilities and potential theory for the brownian path-valued process

Hitting probabilities for Brownian motion on Riemannian manifolds

Invasion probabilities, hitting times, and some fluctuation theory for the stochastic logistic process

Abstract. We consider excursions for a class of stochastic processes describing a population of discrete individuals experiencing density-limited growth, such that the population has a finite carrying capacity and behaves qualitatively like the classical logistic model [22] when the carrying capacity is large. Being discrete and stochastic, however, our population nonetheless goes extinct in fi...

Avoiding-probabilities for Brownian Snakes and Super-brownian Motion Avoiding-probabilities for Brownian Snakes and Super-brownian Motion

We investigate the asymptotic behaviour of the probability that a normalized d-dimensional Brownian snake (for instance when the lifetime process is an excursion of height 1) avoids 0 when starting at distance " from the origin. In particular we show that when " tends to 0, this probability respectively behaves (up to multiplicative constants) like " 4 , " 2 p 2 and " (p 17?1)=2 , when d = 1, d...

Hitting probabilities and large deviations

Let ”Yn•n∈Z+ be a sequence of random variables in R d and let A ⊂ Rd: Then P”Yn ∈ A for some n• is the hitting probability of the set A by the sequence ”Yn•. We consider the asymptotic behavior, as m → ∞, of P”Yn ∈ mA; some n• = P”hitting mA• whenever (1) the probability law of Yn/n satisfies the large deviation principle and (2) the central tendency of Yn/n is directed away from the given set ...

Brownian motion with variable drift: 0-1 laws, hitting probabilities and Hausdorff dimension

By the Cameron–Martin theorem, if a function f is in the Dirichlet space D, then B + f has the same a.s. properties as standard Brownian motion, B. In this paper we examine properties of B + f when f / ∈ D. We start by establishing a general 0-1 law, which in particular implies that for any fixed f , the Hausdorff dimension of the image and the graph of B + f are constants a.s. (This 0-1 law ap...