Recursive interpolation of partially observable random fields
Reduction of absorbing Markov chain
In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a nondecreasing sequence of stopping times. Random walk on the initial...
Refined wing asymptotics for the Merton and Kou jump diffusion models
Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features an interesting "almost power law" tail.
Refinement of the Shannon-McMillan-Breiman theorem for some maps of an interval
Refinement type equations: sources and results
It has been proved recently that the two-direction refinement equation of the form can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation has also various interesting applications....
Refinements of inequalities between the sum of squares and the exponential of sum of a nonnegative sequence.
Reflected backward stochastic differential equation with jumps and random obstacle.
Reflected backward stochastic differential equations with two RCLL barriers
In this paper we consider BSDEs with Lipschitz coefficient reflected on two discontinuous (RCLL) barriers. In this case, we prove first the existence and uniqueness of the solution, then we also prove the convergence of the solutions of the penalized equations to the solution of the RBSDE. Since the method used in the case of continuous barriers (see Cvitanic and Karatzas, Ann. Probab.24 (1996) 2024–2056 and Lepeltier and San Martín, J. Appl. Probab.41 (2004) 162–175) does not work, we develop...
Reflected Brownian motion in a wedge: sum-of-exponential stationary densities.
Reflected diffusions defined via the extended Skorokhod map.
Reflected forward-backward SDEs and obstacle problems with boundary conditions.
Reflected planar brownian motions, intertwining relations and crossing probabilities
Reflecting diffusions and queueing networks.
Reflection and coalescence between independent one-dimensional brownian paths
Reflection coefficients vs partial autocorrelations.
Réflexion discontinue et systèmes stochastiques
Reformed permutations in mousetrap and its generalizations.
Refracted Lévy processes
Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted Lévy processes. The latter is a Lévy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More formally, whenever it exists, a refracted Lévy process is described by the unique strong solution to the stochastic differential equation dUt=−δ1{Ut>b} dt+dXt, where X={Xt : t≥0} is a Lévy...
Regeneration and general Markov chains.
Regeneration in random combinatorial structures.