Related papers: Fluctuation theory for level-dependent L\'evy risk…

The effective dynamics of the low-frequency modes is derived for the O(N) symmetric scalar field theory in the broken symmetry phase. The effect of the high-frequency fluctuations is taken into account at one-loop level exactly. A new…

We study the exact fluctuating hydrodynamics of the scaled Light-Heavy model (sLH), in which two species of particles (light and heavy) interact with a fluctuating surface. This model is similar in definition to the unscaled Light-Heavy…

Motivated by the stochastic Lotka-Volterra model, we introduce discrete-state interacting multitype branching processes. We show that they can be obtained as the sum of a multidimensional random walk with a Lamperti-type change proportional…

We propose a new method to analyze fluctuations in the strength function phenomena in highly excited nuclei. Extending the method of multifractal analysis to the cases where the strength fluctuations do not obey power scaling laws, we…

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of…

In this paper, we will address to the following parabolic equation $$ u_t=\Delta_fu + F(u) $$ on a smooth metric measure space with Bakry-\'{E}mery curvature bounded from below. Here $F$ is a differentiable function defined in $\mathbb{R}$.…

We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…

In this paper we study the convergence of solutions for (possibly degenerate) stochastic differential equations driven by L\'evy processes, when the coefficients converge in some appropriate sense. First, we prove, by means of a…

A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…

We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…

In this paper we consider fractional higher-order stochastic differential equations of the form \begin{align*} \left( \mu + c_\alpha \frac{d^\alpha}{d(-t)^\alpha} \right)^\beta X(t) = \mathcal{E}(t) , \quad t\geq 0,\; \mu>0,\; \beta>0,\;…

In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We…

Conditional independence and graphical models are crucial concepts for sparsity and statistical modeling in higher dimensions. For L\'evy processes, a widely applied class of stochastic processes, these notions have not been studied. By the…

For a positive self-similar Markov process, X, we construct a local time for the random set, $\Theta$, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its…

We extend the work of Kurchan on the Gallavotti-Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes. These include jump processes describing the evolution of stochastic…

First, we present some results about the H\"older continuity of the sample paths of so called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a…

We develop an alternative approach to this field, which was to a large extent developed by Verbeure et al. It is meant to complement their approach, which is largely based on a non-commutative central limit theorem and coordinate space…

The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative Levy process until the passage time of a given level. Their marginal distributions up to an independent exponential time are also…

By using a change of scale and space, we study a class of stochastic differential equations (SDEs) whose solutions are drift--perturbed and exhibit behaviour analogous to standard Brownian motion including to the Law of the Iterated…

We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove…