How to initialize JAXB with SAX properly?

I have a class where multiple threads access it (Something similar to a servlet). There is a method named onEvent which takes an InputStream and unmarshals the input stream received.

To unmarshal, I initialized JAXB and XMLReader in the constructor like below

try {
            jaxbContext = JAXBContext.newInstance(ProductInventory.class);
            jaxbUnmarshaller = jaxbContext.createUnmarshaller();
            final SAXParserFactory saxParserFactory = SAXParserFactory.newInstance();
            reader = saxParserFactory.newSAXParser().getXMLReader();
        } catch (JAXBException e) {
            logger.error("Exception while initializing JAXB", e);
        } catch (SAXException | ParserConfigurationException e) {
            logger.error("Exception while initializing sax xml reader", e);
        }

In the onEvent method I wrote the below code

final InputSource inputSource = new InputSource(inputStream);
final SAXSource saxSource = new SAXSource(reader, inputSource);
SomeClass someClass = (SomeClass) jaxbUnmarshaller.unmarshal(saxSource);

Is the initialization proper? Do I have to initialize the reader evertime a new thread calls onEvent method?