scholarly journals On the last exit times for spectrally negative Lévy processes

2017 ◽  
Vol 54 (2) ◽  
pp. 474-489 ◽  
Author(s):  
Yingqiu Li ◽  
Chuancun Yin ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Occupation Time ◽  
Exit Times ◽  
New Approach ◽  
Last Exit Time ◽  
Spectrally Negative Lévy Processes

Abstract Using a new approach, for spectrally negative Lévy processes we find joint Laplace transforms involving the last exit time (from a semiinfinite interval), the value of the process at the last exit time, and the associated occupation time, which generalize some previous results.

scholarly journals Exit problems for general draw-down times of spectrally negative Lévy processes

2019 ◽  
Vol 56 (2) ◽  
pp. 441-457 ◽  
Author(s):  
Bo Li ◽  
Nhat Linh Vu ◽  
Xiaowen Zhou
Keyword(s):  
Lévy Processes ◽  
Exit Time ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Scale Functions ◽  
Dynamic Level ◽  
Running Maximum ◽  
Potential Measure ◽  
Exit Problems ◽  
Spectrally Negative Lévy Processes

AbstractFor spectrally negative Lévy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find expressions of the Laplace transforms for the two-sided exit problems involving the draw-down time. We also find the Laplace transforms for the hitting time and creeping time over the running-maximum related draw-down level, respectively, and obtain an expression for a draw-down associated potential measure. The results are expressed in terms of scale functions for the spectrally negative Lévy processes.

scholarly journals On transient Markov processes of Ornstein-Uhlenbeck type

1998 ◽  
Vol 149 ◽  
pp. 19-32 ◽  
Author(s):  
Kouji Yamamuro
Keyword(s):  
Markov Processes ◽  
Lévy Processes ◽  
Transition Probabilities ◽  
Levy Processes ◽  
Exit Times ◽  
Linear Drift ◽  
Lévy Measures ◽  
Drift Terms

Abstract.For Hunt processes on Rd, strong and weak transience is defined by finiteness and infiniteness, respectively, of the expected last exit times from closed balls. Under some condition, which is satisfied by Lévy processes and Ornstein-Uhlenbeck type processes, this definition is expressed in terms of the transition probabilities. A criterion is given for strong and weak transience of Ornstein-Uhlenbeck type processes on Rd, using their Lévy measures and coefficient matrices of linear drift terms. An example is discussed.

scholarly journals On the refracted–reflected spectrally negative Lévy processes

2018 ◽  
Vol 128 (1) ◽  
pp. 306-331 ◽  
Author(s):  
José-Luis Pérez ◽  
Kazutoshi Yamazaki
Keyword(s):  
Lévy Processes ◽  
Levy Processes ◽  
Spectrally Negative Lévy Processes

scholarly journals A Subordination Principle on Wright Functions and Regularized Resolvent Families

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Luciano Abadias ◽  
Pedro J. Miana
Keyword(s):  
Fractional Calculus ◽  
Lévy Processes ◽  
Levy Processes ◽  
Laplace Transforms ◽  
Cauchy Problems ◽  
Convolution Properties ◽  
Vector Valued ◽  
Resolvent Families

We obtain a vector-valued subordination principle forgα,gβ-regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results.

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